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Full text of "Analytical Mechanics"

ADDITION AND RESOLUTION OF VECTORS
9
a = ax + ay, ax = a cos 0,
ay == a ^nj a = V^7+
tan 0 =  
(IV)
(V)
(VI)
(VII)
When a has components along all three axes of a rectangular system, Fig. 10, the following equations express the vector in terms of its components.
10.
a = ax+ay+a,. ax = a cos ay = a cos az = a cos 03.
a = Vi^s
(IV) (V)
(VI')
where ai, 0%, and 0$ are the angles a makes with the coordinate axes.
14. Resultant of Any Number of Vectors. Graphical Methods.  The resultant of a number of vectors a, b, c, etc., may be obtained by either of the following methods.
First: move b, without changing either its direction or its. magnitude, until its origin falls on the terminus of a, then